Special transforms of the generalized bivariate Fibonacci and Lucas polynomials

Year 2023, Volume: 52 Issue: 3, 640 - 651, 30.05.2023

Nazmiye Yılmaz , İbrahim Aktaş

https://doi.org/10.15672/hujms.1110311

Cited By: 1

Abstract

This paper deals with the Catalan, Hankel, binomial transforms of the generalized bivariate Fibonacci and Lucas polynomials. Also, some useful results such as generating functions, Binet formulas, summations of transforms defined by using recurrence relations of these special polynomials are presented. Furthermore, certain important relations among these transforms are deduced by using obtained new formulas. Finally, the Catalan, Cassini, Vajda and d'Ocagne formulas for these transforms are also derived.

Keywords

binomial transform, bivariate Fibonacci polynomials, Catalan transform, Hankel transform, Horadam polynomials

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